When the control system into a continuous-time discrete-time, the system becomes a function of the output varied; when the control system becomes nonlinear, the writing by the linear function of the system output becomes more difficult.
Now let me discuss common discrete control system output functions of writing
First, consider the use of intermediate variables to simplify, which is the most common and most common method; For the vast majority of the control system can use this method to simplify, but sometimes there is no simplification out of the situation, this time on the need to simplify the system to break down.
We look at an example:
For this control system, we have found a method directly through the intermediate variable is no way to get the system output. Then we need to be simplified control system based on continuous-time meeting point of the system, as shown
at this time is relatively easy to handle, it is clear that the system has a whole system of continuous feedback loop, and then simplify
the rest the need to use various ways to write output of the function
For the method using the intermediate variables is more troublesome to write, flash write method are proposed function of the output of the sampling some systems to meet specific forms
of course needs to be given before the following equivalent
two equivalents are better appreciated, not then repeat.
Quick Simplifying are now given system functions by:
in a feedback loop:
the input terminal 1. The feedback signal has a sampling switch -> this case no other feedback loop tube sampling switch
2. The whole without the feedback loop sampling switch -> this case no sampled error signal equivalent to the input terminal and the output terminal of the feedback
we can hand the output function
Discrete system sampling switch 1 is determined corresponding to removed continuous output expression system
2 expression in various aspects of product terms required by one asterisk is decided which product term is multiplied with the rest of an item two
binary comparison iff and wherein any of the items are multiplied by a sampling switch to the partition marked * otherwise required phase
multiplication after striking *
3 take the Z-transform the single asterisk is converted into the s number is multiplied by z * only after a number of its Z
transform transfer function equal to the product of Z-transform
Some examples are now given taste
for this control system, meet the above conditions, a continuous system output function
C = G * R / (1 + GH)
Since the deviation signal at a sampling switch, the Z (R & lt * G) = G (Z) R & lt (Z);
GH signal is directly connected in series, the Z (G H) = GH (Z);
the output is
The same for this example
we can get the output
for this system, the condition 2 
is easy to get output
Ok, all of the above conditions are satisfied, and now look at the conditions are not satisfied
in accordance with Theorem, do not qualify, only variable method can be solved. The following solution process
do not satisfy the condition as the above-described system, otherwise it will draw a wrong result
C = G2 * D / (1 + G1G2H)
For this system, but also the conditions are not satisfied
Discrete control system is too much trouble, may encounter in everyday learning is a simple example, you may encounter a variety of situations in the actual project.
